Physical Chemistry Third Edition

498 11 The Rates of Chemical Reactions

PROBLEMS

Section 11.2: Forward Reactions with One Reactant

11.3A hypothetical chemical reaction with a single reactant

and negligible back reaction is 40.0% complete after

185 s at some fixed temperature if the initial concentration

is 0.100 mol L−^1.

a.If the reaction is first order, find the rate constant and

the half-life.

b.If the reaction is second order, find the rate constant

and the half-life.

11.4Write the reaction equation of Example 11.1 in the form

2N 2 O 5 −→4NO 2 +O 2

with the rate equation

−

1

2

d[N 2 O 5 ]

dt

kf′′[N 2 O 5 ]

a.How doesk′′frelate to the coefficientkfgiven in the

example?

b. How does the change in the writing of the reaction

equation affect the half-life of the reaction? Write the

equation relatingt 1 / 2 tok′′f. Find the value of the

half-life of the reaction at the temperature of

Example 11.1.

c.How does the change in the writing of the reaction

equation affect the concentration or partial pressure

of the reactant at a given reaction time? Find the

partial pressure of N 2 O 5 after a reaction time of

100.0 s.

11.5The gas-phase thermal decomposition of bromoethane

follows first-order kinetics. At 500◦C, the rate constant is

equal to 0.1068 s−^1. If the initial pressure of bromoethane

is equal to 1.000 bar, find the partial pressure of

bromoethane at 10.00 s and at 100.0 s if the bromoethane

is decomposed at a constant volume and at a constant

temperature of 500◦C.

11.6For the gas-phase decomposition of N 2 O 3 , the following

data were taken:

time/s: 0 1109 2218

concentration/mol L−^1 : 0.500 0.250 0.125

a.What is the order of the reaction?

b.What is the value of the rate constant?

11.7The gas-phase reaction

SO 2 Cl 2 −→SO 2 +Cl 2

obeys first-order kinetics, withkf 2. 2 × 10 −^5 s−^1 at

320 ◦C.

a.Find the half-life of the reaction at 320◦C.

b.What length of time is required for 90.0% of the

reactant to be consumed at 320◦C?

11.8The gas-phase reaction

N 2 O 5 −→2NO 2 +

1

2

O 2

is found to be first order. The reaction was carried out at

constant temperature of 337.6 K in a constant-volume

container. The initial pressure is equal to 0.100 bar and

no substance is initially present except for N 2 O 5. The

total pressure after 100.0 s of reaction is found to be

0.160 bar.

a.Find the value of the rate constant at this temperature.

b.Find the partial pressure of N 2 O 5 after 100.0 s of

reaction. Neglect the reverse reaction.

c.Find the half-life of the reaction and find the total

pressure at this time.

11.9The following data were taken for the decomposition of

dinitrogen trioxide at some fixed temperature:

t/s: 0 184 526 867 1877

[N 2 O 3 ]/mol L−^1 : 2.33 2.08 1.67 1.36 0.72

Assuming that the reverse reaction is negligible,

determine whether the reaction is first, second, or third

order, and find the value of the rate constant at this

temperature. Proceed by graphing ln(c), 1/c, and 1/c^2 ,or

by making linear least-squares fits to these functions.

Express the rate constant in terms of partial pressure

instead of concentration.

11.10A certain reaction was studied at a fixed temperature. It

was found that if the initial concentration of the single

reactant were equal to 4. 86 × 10 −^3 mol L−^1 , the half-life

of the reaction were equal to 399 s. When the initial

concentration was 2. 28 × 10 −^3 mol L−^1 , the half-life was